a gallon of gasoline costs $3.09 two years ago. Now it costs 1.78. To the nearest percent, what has been the annual rate of decrease in cost?

Question

a gallon of gasoline costs $3.09 two years ago. Now it costs 1.78. To the nearest percent, what has been the annual rate of decrease in cost?

Answer 1

Let x be the amount that we multiply the old amount by to obtain the new amount. Then $3.09 times x times x should yield $1.78

 

So, x^2 = 1.78/3.09 = 0.5761

 

If x^2 = 0.5761 then x = 0.759

 

Now, multiplying by 0.76 is the same as reducing the price by 24%. This implies that the decrease in price as a percentage is about 24% annually.

 

Check: 3.09 (.24) = 0.7416 or 0.74 rounded.

3.09 - 0.74 = 2.35 (the price after one year)

 

2.35 (.24) = 0.564 or 0.56 when rounded.

2.35 - 0.56 = 1.79 (a bit high due to rounding down twice.)

Answer 2

Rate of decrease =(3.09 - 1.78) / 3.09 * 100 

 

= 131 / 3.09

 

= 42.39482

 

Rate of annual decrease = 42.39482 / 2 

 

= 21 percent to the nearest percent .